how much is the edge of shuffle tracking?

#1
what the max possible edge that shuffle tracking can achieve for 6-deck shoe game? Do most pro counters use shuffle tracking to increase their edge? Is any classical book on shufftle tracking that I am supposed to read to learn this tech?

thanks
 

The Mayor

Well-Known Member
#2
A fairly ignorant response

>what the max possible edge that shuffle tracking can achieve for 6-deck shoe game?

If you track perfectly, and know every card and the exact order... well, I am not sure what your question is here. Maybe you are asking what kind of edge a reasonably good ST'er can get. That depends on the shuffle he is attacking and his skill with that particular shuffle. But, it is a much stronger technique than card counting. If you track a single Ace perfectly and "own" the table so that you can steer cards whereever you wish, you can get close to a 50% edge. If you are just talking about tracking segments of paint (as most ST'ers do), then in practice the upper bound is about 5%.

>Do most pro counters use shuffle tracking to increase their edge?

No.

>Is any classical book on shufftle tracking that I am supposed to read to learn this tech?

Read EVERY book. The books that are out there don't begin to teach you all you need to know. But there are so few, certainly you should read them all. It is a very long road. Those who travel it and succeed are true warriors. I know a couple of infrequent posters here who are on that road, and if they want to chime in, it would be very appreciated.

If you go to "The Best Posts" on this site, there are a couple of great articles by Sonny.

--Mayor
 
#3
thanks a lot and...

thanks a lot for the useful info! I do have a few more questions though.

I am quite new to ST. In your response, it seems to me that there are a few kind of ST tech. so what the the major kinds of ST that most BJ pro use to incrase their profit?

For books talking about ST on market, I only know there is a chapter talking about it in Blackbelt in Blackjack by Arnold Snyder. Is The Blackjack Shuffle Tracker's CookbooK by him still on the market now? Any other books that we can buy about ST now?

Also, what about the edge for Cut Cards and Ace Sequencing? Any book or material that we can find to learn these tech?

thanks a billion!
 

Sonny

Well-Known Member
#4
Some recomendations

> I am quite new to ST. In your response, it seems to me that there are a few
> kind of ST tech. so what the the major kinds of ST that most BJ pro use to
> incrase their profit?

There are several different variations on shuffle tracking. The link that the mayor mentioned above describes cut-off tracking, where you track the cards that are behind the cut card. It is probably the easiest and most often useful method of tracking a shuffle. It is the best place to start.

There is also segment tracking, where you track several segments of the shoe and follow them through the shuffle. Often times knowing the location of just one or two "rich" or "poor" spots will be all the information you need. You can also achieve this through card sequencing or slug sequencing.

Full-blown shuffle tracking requires documenting every segment of the shoe and following them through the shuffle so that you have a fairly accurate representation of the shuffled shoe. It is a very difficult technique to master and you will rarely find an opportunity to use it, but it is also the most powerful variation.

> For books talking about ST on market, I only know there is a chapter talking
> about it in Blackbelt in Blackjack by Arnold Snyder. Is The Blackjack Shuffle
> Tracker's CookbooK by him still on the market now? Any other books that we can
> buy about ST now?

Those are both great books. You could also check out Mason Malmuth's "Blackjack Essays" for more information about cut-off tracking (he calls it "card domination") as well as some other decent information. The Cookbook is still available in certain stores and on the internet (amazon.com and advantageplayer.com are both good sources). There are also a few articles on bjmath.com but they can be a bit hard for newbies to understand. There are a few other books that I could mention but they are either somewhat unreliable (J. Patterson) or too advanced for beginners (McDowell) so I therefore do not recommend them to you.

Unfortunately, you will have to do most of the work yourself. You should read as much about it as you can, but eventually you are just going to have to do your own research in order to find ways of making it work for you. Each casino will offer different opportunities and will require you to customize the techniques for their shuffling procedures. Once you understand how these techniques work you will know how to recognize the weaknesses and spot the opportunities in certain casinos.

> Also, what about the edge for Cut Cards and Ace Sequencing?

The advantages for these techniques completely depend on how accurately you can perform them and how often the opportunities arise. Any inaccuracies (and there will be plenty, even for experienced players) will reduce or possibly destroy your edge. On the other hand, even with perfect prediction you will not make any money unless you find games that can be tracked. There is an enormous amount of work that must be done in order to use these techniques. By the time you are ready to try them in actual casino play you will already know how much of an advantage you can expect.

> thanks a billion!

No problem. Welcome to the site!

-Sonny-
 
#5
and the very frustrating part

will be, that the dealer will 4 times in a row turn an ace on his ten
for a black jack, or the slug you tracked is only at the bottom loaded with pictures, and all your spots will receive a small card as the second card, and the dealer will make 17 out of a 6.

gambler.
 
#7
Effortless cutoff tracking

There is one technique for manipulating a shoe that requires no effort whatsoever at the table. Unfortunately it only works when you have the cut card.

For every shuffle there exists two cut points such that one will maximize the amount of the cutoff that will be dealt in the next round, and one will minimize it. For example in one place I play, the cut point for maximum cutoff is 1.5 decks from the front, and for minimum it is 3.5 decks. All I need to remember is those two numbers. So if the running count at the end of the shoe is positive the cut card goes 1.5 back, and if it is negative it goes 3.5 back. That's the simplest form of shuffle tracking and probably the least powerful. But it's a good place to start if you want to get into analyzing and tracking shuffles.
 
#8
and/or. . .

in addition to Sonny's suggestions, another route is to pick up CVBJ and CVShuffle and teach yourself by playing around with the shuffle analysis tools. Actually, I think you could learn a lot just by picking up the demo version, which will give scrambled results but could teach you a lot of the main concepts.

BTW, you might not be able to find some of the answers you're after anywhere. Research on things like ace prediction isn't available (to the public, at least) anywhere near the scale of traditional card counting. And unfortunately the technique doesn't lend itself particularly well to quantitative analysis, at least in terms of producing a clear cut SCORE or ev. Too many variables: Are you only tracking one ace per six deck shoe, or all 24? Are you able to track the ace precisely (ev=52%) or to the nearest 4 cards (ev=13%)? Are you able to suddenly jump your bet from $500 throughout the shoe to 7 hands of $10,000, like the MIT guys, or are you playing in a casino that is watching out for that sort of thing?

So I think it's hard to compare to card counting.
My solution: Do both :)
 
#10
one idea...

This all depends on the shuffle used, how many decks are cutoff, etc.

For example, at the first "indian store" where the "shuffle-tracking" concept suddenly popped into my head, we were in a 6d shoe, with 1.5 decks cut off. The shuffle was a single riffle, with the cut-off 1.5 decks stuck on the top of the discard tray.

With a big + count left, the last 1.5 decks are rich. After that single riffle, the bottom 3 decks are 1/2 as rich since the 1.5 decks are now diluted with 1.5 decks with an unknown count. So given the cut-card, where do you insert it? If you insert it 3 decks from the front, you just moved the 3-deck rich segment to the front of the shoe. So that is a good reason for 3 decks from the front for this particular game. Play 3 decks, then get up and leave. Or, if the count was negative when the shuffle card came out, put the cut card 1.5 decks from the back, which cuts one half of the diluted (and 10-poor section) to the back of the shoe, the other 1.5 decks go to the front. Now you don't play, or you min bet if you have to, for 1.5 decks, until you get to the other 3 decks, which must have a count exactly the opposite of the 10-poor half and you can ramp your bet to that count level without worrying about counting or anything else.

Notice this would change if the penetration changed to 5.0/6.0 decks dealt. Or if you play an 8D shoe, etc. But for a particular game with particular penetration, when you cut you can maximize your advantage. If someone else cuts, you simply have to remember whether (a) you start off in a rich or poor section of the shoe, and (b) how many decks to play before this section is gone.

That's sort of the idea he was getting at I assume... Of course different shuffles, and plugging the undealt cards changes all of that significantly. And hardly anyone does a single riffle today because of this.

AM - if I mangled your idea, by all means correct this. :)
 
#11
It just changes the composition of the shoe, in the long run

My method was to simulate the shuffle using CVShuffle and see where the cutoff cards are most and least likely to end up in the next shoe. Placing the cut card at 1.5 puts the maximum of the cutoff cards back into play, and placing it at 3.5 puts the maximum of the cutoff cards back behind the cut card again. It's a function of that particular shuffle and has to be recalculated for every shuffle.

For shuffles that use a plug, a more effective (but slightly harder) method is to do the exact same thing but for the first deck or so where the dealer usually doesn't insert a plug. It's only harder because you have to remember what the count was at that point, not what it was when the cut card comes out.

It doesn't buy you all that much, just on the average adds/subtracts a few cards from play. But if you were playing a shoe game where you knew a couple of 5's had been thrown in the trash can, pretty good deal no? Once you calculate those two points, it's basically a freebie.
 
#12
When I first started this tracking approach...

I kept track of each deck for a 6 deck shoe, then I could calculate how each deck was affected when mixed with its "matching" deck from the second stack. Wasn't too hard, but since the single-riffle is pretty rare (I played at one Indian store where a dealer was _very_ old and a single riffle took him a couple of minutes so he still does it when no one is looking) I quit worrying about it. And you are right, CV shuffle will point out some things that are not expected when you first think about this process...
 

alienated

Well-Known Member
#13
A couple of examples

<em>It doesn't buy you all that much, just on the average adds/subtracts a few cards from play. But if you were playing a shoe game where you knew a couple of 5's had been thrown in the trash can, pretty good deal no? Once you calculate those two points, it's basically a freebie.</em>

Nice post. As you say, it doesn't buy you much, but it is better than nothing for virtually no effort.

A couple of examples might give other readers some idea of the likely value of this approach.

The tables below use the following key:

d = shoe size (in decks)
p = penetration point (i.e., the amount of decks before the shuffle card)
k = the amount of cutoffs
a = the amount of cutoffs cut into play
Nm = the expected amount of cutoffs in play with no smart cutting
Dv = deviation from the normal amount of cutoffs in play with smart cutting
AvBig = average number of big cards cut into play when cutoffs rich
AvSmall = average number of small cards cut out of play when cutoffs poor
N = number of pseudo decks in the played shoe (only relevant if the NRS approach is used)
r = multiplier (only relevant if the NRS approach is used)

(NB. I have arbitrarily assumed that when the count of the cutoffs is zero, the player cuts to minimize the number of cutoffs in play.)

Code:
                                Table 1

d   p   k    a      Nm      Dv      AvBig    AvSmall     N       r
8   6   2   2.00   1.50    0.50     2.17                7.71   -0.43
            1.90   1.50    0.40     1.74                7.81   -0.35
            1.80   1.50    0.30     1.30                7.89   -0.26
            1.75   1.50    0.25     1.09                7.93   -0.22
            1.70   1.50    0.20     0.87                7.95   -0.18
            1.60   1.50    0.10     0.43                7.99   -0.09
            1.50   1.50    0.00     0.00                8.00    0.00
            1.40   1.50   -0.10               0.39      7.99    0.09
            1.30   1.50   -0.20               0.78      7.95    0.18
            1.25   1.50   -0.25               0.98      7.93    0.22
            1.20   1.50   -0.30               1.18      7.89    0.26
            1.10   1.50   -0.40               1.57      7.81    0.35
            1.00   1.50   -0.50               1.96      7.71    0.43
            0.90   1.50   -0.60               2.35      7.59    0.51
            0.80   1.50   -0.70               2.74      7.46    0.58
            0.75   1.50   -0.75               2.94      7.38    0.62
            0.70   1.50   -0.80               3.14      7.31    0.65
            0.60   1.50   -0.90               3.53      7.14    0.71
            0.50   1.50   -1.00               3.92      6.97    0.77
            0.40   1.50   -1.10               4.31      6.78    0.83
            0.30   1.50   -1.20               4.70      6.59    0.88
            0.25   1.50   -1.25               4.90      6.50    0.90
            0.20   1.50   -1.30               5.10      6.40    0.92
            0.10   1.50   -1.40               5.49      6.20    0.96
            0.00   1.50   -1.50               5.88      6.00    1.00



                                Table 2

d   p   k    a      Nm      Dv      AvBig    AvSmall     N       r
6   4   2   2.00   1.33    0.67     3.08                5.33   -0.67
            1.90   1.33    0.57     2.62                5.50   -0.58
            1.80   1.33    0.47     2.16                5.65   -0.49
            1.75   1.33    0.42     1.93                5.72   -0.45
            1.70   1.33    0.37     1.70                5.78   -0.40
            1.60   1.33    0.27     1.23                5.88   -0.29
            1.50   1.33    0.17     0.77                5.95   -0.19
            1.40   1.33    0.07     0.28                5.99   -0.07
            1.33   1.33   -0.00     0.00                6.00    0.00
            1.30   1.33   -0.03               0.14      6.00    0.04
            1.25   1.33   -0.08               0.35      5.99    0.09
            1.20   1.33   -0.13               0.55      5.97    0.15
            1.10   1.33   -0.23               0.97      5.91    0.26
            1.00   1.33   -0.33               1.38      5.82    0.36
            0.90   1.33   -0.43               1.80      5.70    0.46
            0.80   1.33   -0.53               2.21      5.56    0.56
            0.75   1.33   -0.58               2.42      5.48    0.60
            0.70   1.33   -0.63               2.63      5.39    0.64
            0.60   1.33   -0.73               3.04      5.21    0.72
            0.50   1.33   -0.83               3.46      5.02    0.78
            0.40   1.33   -0.93               3.87      4.82    0.84
            0.30   1.33   -1.03               4.28      4.61    0.89
            0.25   1.33   -1.08               4.49      4.51    0.92
            0.20   1.33   -1.13               4.70      4.41    0.94
            0.10   1.33   -1.23               5.11      4.20    0.97
            0.00   1.33   -1.33               5.53      4.00    1.00
EXAMPLE from Table 2:

The second table says, for instance, that if you are playing a 6-deck game where 4 decks are dealt, and the maximum amount of cutoffs that can be cut into play is 1.8 decks (out of a possible 2 decks), then of the times in which the cutoffs are rich, on average you will cut in 2.16 extra big cards.

Of course, if the cutoffs are poor, you will want to minimize the number of cutoffs in play. Suppose the minimum amount of cutoffs that can be cut into play is 0.75 decks. Then of the times in which the cutoffs are poor, on average you will cut 2.42 extra small cards out of play.

Obviously the further you can get away from normal dispersion of the cutoffs the better. If the cutoffs were distributed perfectly evenly throughout the shoe, the deviation from normal dispersion would be zero, and the gains from this approach would also be zero.

The simplest way to approach the situation described in this example would be to treat the game in the normal fashion; i.e., as a 4/6 game and an IRC of zero. Your indices and betting will err on the side of caution, which is not a serious problem, given that the shift in true-count distribution will only be subtle in the average case.

Improvement can be obtained by using the NRS parameters. When the player can cut 1.8 decks of cutoffs into play, table 2 indicates that the appropriate choice of N is 5.65 and r is -0.49. So, for instance, if the running count of the cutoffs is -6, set your IRC to +3 and treat the game roughly as if it were a 4/5.65 deck game.

Similarly, when the player cuts a minimum of 0.75 decks of cutoffs into play, the appropriate parameters are N = 5.48 and r = 0.6. If the running count for the cutoffs is +7, set your IRC to +4 and treat the game roughly as if it were a 4/5.5 deck game.

NOTE: There is a subtle but important difference between a literal game with N decks and the pseudo (NRS) game we are playing here. Specifically, with the NRS pseudo game we need to be sure that we will complete the round without the shuffle card being reached. This is because the cutoffs supposedly excluded from play due to the player cut come back into play once the shuffle card has come out. In other words, only use the NRS running count if the entire round can be dealt before the appearance of the shuffle card. (Aside: It is possible to treat the round involving the shuffle card as a boundary and base the bet on this boundary information, which I have described elsewhere.)

Although on average the impact of this sort of cutting on the true-count distribution will be small, in individual cases the effects can be more worthwhile. Continue considering the 4/6 game. From time to time the 2 decks of cut offs will have more extreme running counts. A cutoff running count outside the range [-6,+6] will occur about 37% of the time. About 15% of the time the cutoffs will have a running count outside the range [-10,+10].

This means that some shoes will be much more appealing than the average. For instance, if the cutoffs have a running count of -10 and the maximum amount of cutoffs that can be cut into play is 1.8 decks, then you are entitled to set your IRC to +5, giving an initial true count of almost +1 for the 5.65 deck pseudo game. If the cutoffs have a running count of +/-15 (cases this extreme or more extreme occur about 4.7% of the time), then you can set your IRC to +7 or +8, depending on the precise case.

Needless to say, if the cutoffs are more evenly dispersed throughout the shoe, the gains from this approach are even more modest. If the maximum amount of cutoffs that can be cut into play is only 1.6 decks, then in cases where the cutoffs are rich, the player will only cut an average of 1.23 extra big cards into play. The gains from the NRS approach are also reduced, N rising to 5.88 and r shrinking to -0.29. Then even a running count of +/-10 for the cutoffs would only justify an IRC of about +3 and an initial true count of just over +0.5. Just as obviously, if the cutoffs are less evenly dispersed, the gains can be greater than in the examples discussed above.
 
#15
A small question:

How frequently do you find games with this degree of trackability?
Is this applyable to most hand suffled games, or only simple shuffles?

Thanks again for your great contributions.
 

alienated

Well-Known Member
#17
A vague answer and some other remarks

It won't always be very effective to focus on the cutoffs. As Automatic Monkey says, plugging may contribute to a very even dispersion of the cutoffs throughout the shoe. Even if the cutoffs are topped, they may still get very evenly dispersed.

But there is a bigger point in all this, which was stated explicitly by Automatic Monkey: the same approach can be used for any segment of the shoe, not just the cutoffs. So for some shuffles, as is pointed out, you may find that the first deck provides a better opportunity (i.e., is quite unevenly dispersed throughout the shoe). Or perhaps the last dealt deck is more unevenly dispersed. Or perhaps some other section of the shoe. It doesn't really matter. The trick is to find the best choice for a given shuffle.

The method is applicable to quite complicated shuffles, although its power will decline the more evenly the targeted segment is dispersed throughout the shoe.

Here is one other point to keep in mind. It may be better to focus on a smaller segment of the shoe that is contained entirely within a certain section of the new shoe, rather than picking a larger segment that will be spread (albeit unevenly) throughout the entire shoe.

For instance, suppose that for a particular shuffle we have two choices. One option is to take advantage of a property that 80% of the first deck goes into one half of the new shoe (let's assume a 6-deck shoe). The other option is to use another property that 100% of the first 33 cards go into one half of the shoe. Which is the best option?

The two options have the following parameters:

Code:
Option    N     |r|      x     y    IRC(x)  IRC(y)  IRC>|6|  IRC>|10|
   1     5.60   0.67   -4.31  4.95   3.32    2.90    14.2%     1.2%
   2     5.37   1.00   -3.51  4.15   3.51    4.15    17.3%     2.7%
The meaning of the notation is as follows:

N = number of pseudo decks (using NRS) (i.e., treat the best half of the 6-deck shoe as containing this many pseudo decks)
|r| = absolute value of the multiplier (using NRS)
x = average running count of the tracked "slug" when its count is negative and we want to cut it as much as possible into play (the "slug" in option 1 is the first deck of the shoe; in option 2 it is the first 33 cards)
y = average running count of the tracked "slug" when its count is nonnegative (includes the zero case) (here we would cut as much of the slug as possible out of play)
IRC(x) = average initial running count when the slug count is negative = r*x
IRC(y) = average initial running count when the slug count is nonnegative = r*y
IRC>|6| = percentage of shoes for which the IRC is outside the range [-6, 6]
IRC>|10| = percentage of shoes for which the IRC is outside the range [-10, 10]

Let's compare the two options. With option 1 we track a whole deck, but only 80% of it is retained in one half of the shoe. The other 20% spills out into the other half of the shoe. In this situation we are entitled to play the best half as if it is a 3/5.6 deck game. On average, the IRC will be set to +3, giving an average initial true count of +0.54. Sometimes the situation will be better. For instance, we get IRC > |6| about 14.2% of the time, giving us an initial true count exceeding +1. In a tiny 1.2% of cases we get IRC > |10|, giving an initial true count approaching +2.

With option 2 we track less cards (33 instead of 52), but all of these cards are retained in one half of the shoe. This enables us to treat the best half as a 3/5.4 deck game. The average IRC will be +3 when the 33 cards are cut into play and +4 when they are cut out. We get IRC > |6| about 17.3% of the time and IRC > |10| a smaller 2.7% of the time.

On balance, option 2 appears to be the slightly better one in the specific example we have considered. Its effective penetration is slightly better (3/5.4 versus 3/5.6), its average IRC is marginally higher, and extreme IRCs are more frequent. (Note: Although x and y are bigger in absolute value for option 1, these larger magnitudes for x and y translate into smaller IRCs because the multiplier is smaller with option 1 than option 2 (0.67 < 1).

Even so, either of these options is a worthwhile play. More generally, changing the assumptions of the examples will alter the relative results. For instance, if 90% (rather than 80%) of the first deck ended up in one half of the shoe, or if only the first 23 (rather than 33) cards ended up in one half of the shoe, option 1 would become relatively more attractive. The purpose of the above comparison is simply to show that there are various options when considering how to approach a particular shuffle.

Lastly, keep in mind that your "slug" does not necessarily have to be a literal slug. That is, a 52-card slug does not have to be 52 consecutive cards. It might be made up of cards 1-26 and 79-104. Or it might be made up of the first and last dealt half decks. It doesn't matter. The main questions are: 1) How many cards do you have a precise count on?; and 2) How many of them end up in a certain segment of the new shoe?
 
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